If you've watched any of the popular programs on the universe you've probably seen spacetime modelled by a rubber sheet, and the effect of gravity modelled by the dents made in the rubber sheet by masses moving around on it. Like all analogies this one can be misleading (sometimes dangerously misleading!) but lets stick with it for the moment.
Unlike a rubber sheet, spacetime is infinitely stretchable. In fact at the singularity in the centre of a black hole spacetime does get infinitely stretched (though quantum gravity probably steps in before the curvature becomes infinite). That means you could have some areas of your rubber sheet that are reasonably flat, while there are others that are stretched into all sorts of strange shapes.
No matter how contorted your rubber sheet gets, it is still possible to imaging taking a marker pen and drawing a line from any point on the sheet to any other point. But in the real universe we can't move faster than light, so while we can indeed imagine a line connecting any bit of the universe to any other, you may need to travel faster than light to trace out such a path. This is exactly what happens in a black hole. The black hole hasn't been disconnected from the rest of the universe, and you can imagine lines that lead out of the black hole, but you'd need to move faster than the speed of light to follow these lines. That's why you can't get out of a black hole, because you can't travel faster than light.
This is basically the situation with the multiverse. There are various ideas about how multiverses might form, but the most popular is probably based on eternal inflation. We probably need to abandon the rubber sheet analogy at this point, but you can think of eternal inflation as rapidly stretching spacetime. In fact it's being stretched much much faster than anything we see in our universe at the moment. However some regions of spacetime stop stretching and form regions of approximately flat spacetime, and that's where we live.
In eternal inflation spacetime hasn't been torn or ruptured in any way, and in principle there are continuous lines that lead out of our region of flat spacetime through the raipdly stretch areas and into another flat region i.e. another "universe". However the limit of the speed of light means that there is no way that anything, not even light, could ever get out of our "universe" and into one of these other "universes". That's why you'll hear them described as separate universes.
So forget any notion of inter-universe portals that you might have read in science fiction books. It's all just one universe really and the multiverse is really just separate regions of flat spacetime.